Question

Find ratio of angular speeds of second hand and minute hand?

Answer 1

The second hand of a clock completes one full rotation in 60 seconds, while the minute hand completes one full rotation in 60 minutes, or 3600 seconds. Therefore, the ratio of the angular speeds of the second hand and minute hand is:

Angular speed of second hand / Angular speed of minute hand = (2π radians / 60 seconds) / (2π radians / 3600 seconds)

Simplifying this expression:

Angular speed of second hand / Angular speed of minute hand = (2π / 60) / (2π / 3600) = (2π / 60) x (3600 / 2π) = 3600 / 60 = 60/1

Therefore, the ratio of the angular speeds of the second hand and minute hand is 60:1. This means that the second hand rotates 60 times faster than the minute hand.